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. zeno of elea, who predated aristotle, wrote a series of paradoxes that still give us pause today. one of the best known tells the story of achilles and the tortoise and their race. achilles is such a fast runner, he gives the tortoise a head start. they each run at constant speeds: achilles very fast, the tortoise very slow. after a finite amount of time, achilles gets to where the tortoise started, but the tortoise will have moved on. it takes achilles a finite amount of time to get to the tortoise's next spot, but by the time he arrives, the tortoise will have moved on from there as well. and so on, and so on, over and over again, ad infinitum. despite what our senses tell us, zeno is telling us that achilles will never catch the tortoise. zeno's paradoxes were a big problem for the greek philosophers, and they did just about everything they could to avoid confronting the infinite because they based their arithmetic and their entire worldview on something much more tangible: geometry. their notion of the mathematical and the physical was intimately linked to the practice of measurin
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